Few acts rewrite the comedy rulebook as determinedly as Sam Simmons. The Aussie arrives on stage dressed as an astronaut and swiftly lays down his idiosyncratic law: scissors will not be tolerated during the gig, he tells us. Nor the colour yellow. And there are to be absolutely no cats – except those with their innards on display.

It's just the tip of the iceberg in a breathlessly inventive psycho-comedy that thrives off Simmons's warped whimsicality. Purporting to answer questions sent to him by fans, this agonised uncle rather treats us to a montage of elliptically surreal, jarringly abrupt vignettes that cumulatively suggest a series of The Mighty Boosh run through a shredder. There are air guitar solos, pine-cone people, life-affirming llamas and visions of Toadfish from Neighbours in spilt supermarket salsa.

But more compelling than any single moment of lunacy is the running thread of Simmons's brazenly insecure persona. One minute he's barking at us like a demented drill sergeant; the next, retreating into disaffected self-pity. To paraphrase the Bard, here is a man who could be bounded in a nutshell and count himself a king of infinite idiocy – were it not that he had some seriously bad neuroses. Indeed, he saves the best for last: a visceral lament for the "nasty" modern world's lack of silliness that strikes a note of forlorn desperation and exerts an emotional pull you never saw coming. "A lot of you are still very uncertain tonight – I WILL WIN," he assures us, and I, for one, find myself dazzled, and drained into submission.

Back on Planet Earth, Sarah Millican is gracing the festival for only two weeks this year, her appearance at the cavernous Assembly Hall a marker of her newly minted star cachet. But though the weight of expectation hangs heavy, she hasn't left anything to chance: her new show comes broadly themed around her risk-averse nature, from her childhood fear of Space Dust to her belief that "starting on a new tea towel" represents the apogee of excitement. Tenuous or not, it's a conceit that's sorely tempting fate, considering just how cautious much of this set really is: see tried-and-trite blather about the trials of losing weight and the perils of sharing a bed. Her blithely no-nonsense attitude to sex remains eminently relishable – see a hilarious account of arousal by custard – and I like the way she can segue from sweetness to savagery in an instant. But a tastelessly brilliant closing humdinger about a murder report only makes you wish she'd dare to deviate more often, on stage if not in life.

Amid the Fringe's usual barrage of second-rate scatology, Diane Spencer's All-Pervading Madness really shows how to make filth fly. Making her sophomore solo festival appearance, Spencer spins a shaggy and shag-filled dog story about a disastrous after-hours journey home, marred by bursting blood vessels, "pussy banging" girlfriends and "hobo-cops". Gleefully horrific characterisations abound, but the real pleasure lies in the digressions laying bare Spencer's own grotesquery. She may sound refined, but wait till you hear about her trick with a cooked sausage: think a Home Counties head girl as imagined by John Waters. It's a tiggerishly enjoyable, self-assured set, even if it does trail off a touch in the closing minutes.

And talking of Edinburgh sophomores, a quick word on Nick Helm: mixing cock-rock swagger, an ear-blasting bellow and the emotional dilapidation of a young Johnny Vegas, Helm turns things up to 11 with the riotous Dare to Dream. I wouldn't be surprised to see him, Simmons or Spencer among this week's Comedy Award nominees.

Meanwhile, 2011's misplaced hype award must surely go to Hot Tub with Kurt and Kristen, the vanilla variety show of Kristen "Flight of the Conchords" Schaal and Kurt Braunohler, on a two-week vacation from New York. Attending their first night, I am warned that a curtailed technical rehearsal means there may be some edges. If only, frankly. Despite the show's cult status and the hipster-ish, electro-rap house band, the whole thing feels as sterile as a second-string, US network sitcom, with laboured badinage, plasticky cheer and perfunctory links to the guest comics. The highlight is Schaal: dead-eyed and droningly disturbed as she tells us how "I don't play guitar ... I just play a man like one..."; she leaves you wondering about the darkly, compelling solo gig that might have been.

For variety with real verve, however, there's been Alex Horne and his trusty band the Horne Section at the Assembly's Spiegeltent. An uproarious, late-night knees-up involving jazzy improvisation, audience games and star cameos, on the night I see them highlights include Paul Foot's musically accompanied "disturbances" and the Section's pitch-perfect parody of a boy-band anthem. That compère Horne manages to shine against this noisy backdrop of musical high jinks speaks volumes about the much-loved Fringe veteran's stage presence. Also here with Seven Years in the Bathroom at the Pleasance Dome – a typically busy and buoyant solo show which finds him replicating the life of an average male in an hour – he possesses the kind of extreme congeniality that light entertainment producers would do well to harness.

Finally, forgive me a cheeky step outside my remit: for though John Peel's Shed is certainly comic, humour is but a peripheral pleasure of John Osborne's utterly delightful paean to radio. Beginning with his victory in a competition to win a box of the legendary DJ's vinyls, it explores the medium's transformative role in his life, whether providing a feeling of belonging to his shy teenage self or a sense of purpose to his drifting graduate one (via the station-a-day listening mission he embarked on for his 2009 book Radio Head: Up and Down the Dial of British Radio). The spectre of Alan Partridge inadvertently looms over his account of a stint presenting a show at a Norwich community radio station, but there's nothing absurd about his undiluted joy at receiving a message of thanks from a contented listener. And though Osborne is a diffident performer, his sincerely halting delivery is just the thing for a show that wears its heart on its record sleeve.